Find the Derivative - d/dx cos(8x)

Problem

d(cos(8*x))/d(x)

Solution

1. Identify the outer function and the inner function to apply the Chain Rule. The outer function is cos(u) and the inner function is u=8*x

2. Apply the derivative of the outer function. The derivative of cos(u) with respect to u is −sin(u)

3. Apply the Chain Rule by multiplying the derivative of the outer function by the derivative of the inner function, (d(8)*x)/d(x)

4. Differentiate the inner function. The derivative of 8*x is 8

5. Simplify the expression by multiplying the terms together.

Final Answer

d(cos(8*x))/d(x)=−8*sin(8*x)

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